A088163 Numbers for which rotating one binary place to the right less rotating one binary place to the left is equal to zero.

0, 1, 2, 3, 7, 10, 15, 31, 42, 63, 127, 170, 255, 511, 682, 1023, 2047, 2730, 4095, 8191, 10922, 16383, 32767, 43690, 65535, 131071, 174762, 262143, 524287, 699050, 1048575, 2097151, 2796202, 4194303, 8388607, 11184810, 16777215, 33554431, 44739242, 67108863

Offset: 0

Author

Robert G. Wilson v, Sep 13 2003

Keywords

• nonn
• easy

Comments

n is a member iff n is of the form 2^n -1 (A000225) or A000975(2n).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,5,0,0,-4).

Crossrefs

Cf. A000225, A000975.

Programs

Mathematica

f[n_] := FromDigits[ RotateRight[ IntegerDigits[n, 2]], 2] - FromDigits[ RotateLeft[ IntegerDigits[n, 2]], 2]; Select[ Range[33560000], f[ # ] == 0 &]
(* Or *) Union[ Join[ Table[2^n - 1, {n, 0, 25}], Table[ Ceiling[2(2^n - 1)/3], {n, 2, 24, 2}]]]
LinearRecurrence[{0,0,5,0,0,-4},{0,1,2,3,7,10},40] (* Harvey P. Dale, Feb 20 2022 *)

PARI

concat(0, Vec(x*(1+x)*(1+x+2*x^2) / ((1-x)*(1+x+x^2)*(1-4*x^3)) + O(x^50))) \\ Colin Barker, May 14 2016

Formula

Numbers n such that A038572(n) - A006257(n) = A088161(n) = 0.

From Colin Barker, May 14 2016: (Start)

a(n) = 5*a(n-3)-4*a(n-6) for n>5.

G.f.: x*(1+x)*(1+x+2*x^2) / ((1-x)*(1+x+x^2)*(1-4*x^3)).

(End)